Ruin probability in a risk model with variable premium intensity and risky investments

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin pr...

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Bibliographic Details
Published in:	Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica Vol. 35; no. 3; pp. 333 - 352
Main Authors:	Mishura, Yuliya, Perestyuk, Mykola, Ragulina, Olena
Format:	Journal Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2015
Subjects:	existence and uniqueness theorem explosion time exponential bound infinite-horizon ruin probability risk process risky investments stochastic differential equation supermartingale property variable premium intensity
Online Access:	Get full text
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Summary:	We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.
ISSN:	1232-9274
DOI:	10.7494/OpMath.2015.35.3.333